Hypothesis testing and OLS Regression

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Hypothesis testing and OLS Regression

NIPFP 14 and 15 October 2008

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Overview

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A Monte-Carlo simulation Model Specification

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

The OLS estimator continued

As we discussed yesterday, the OLS estimator is a means of obtaining good estimates of 1 and 2, for the relationship Y = 1 + 2X1 +

Let us now move towards drawing inferences about the true 1 and 2, given our estimates ^1 and ^2. This requires making some valid assumptions about Xi and . These assumptions also evoke certain useful statistical properties of OLS, as constrasted with the purely numerical properties which we saw yesterday.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumptions of OLS regression

Assumption 1: The regression model is linear in the parameters. Y = 1 + 2Xi + ui . This does not mean that Y and X are linear, but rather that 1 and 2 are linear.

Introduction Assumptions of OLS regression Gauss-Markov Theorem Interpreting the coefficients Some useful numbers A M

Assumptions of OLS regression

Assumption 1: The regression model is linear in the parameters. Y = 1 + 2Xi + ui . This does not mean that Y and X are linear, but rather that 1 and 2 are linear.

Assumption 2: X values are fixed in repeated sampling.

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